Texturing with remesh modifier
If you're only using the Remesh modifier with the purposes of subdividing the model then the 'Subdivision Surface' modifier set to 'Simple' subdivision will probably be better. 

This will subdivide the object in a similar manner to doing W> Subdivide in edit mode, but will not change the shape of the object like the default 'Subdivision Surface' modifier will:



At least on a simple test, it doesn't seem to distort the UVs and leaves them intact.